Question

(a) Define mutual inductance and write its S.I. unit.
(b) A square loop of side ‘a’ carrying a current I2 is kept at distance x from an infinitely long straight wire carrying a current I1 as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Answer 1

Answer:

Part a)

SI unit of mutual inductance is Henry (H)

Part b)

Net force on the loop due to long wire is

$F = \frac{\mu_o i_1 i_2 a^2}{2\pi (x)(x + a)}$

Explanation:

Part a)

When EMF induced in a coil due the the change in flux of its adjacent coil then this phenomenon is induction of EMF is known as Mutual Inductance

Its SI unit is Henry(H)

Part b)

Magnetic field due to long straight wire given as

$B = \frac{\mu_o i_1}{2\pi r}$

Now magnetic force due to magnetic field of long wire to the nearest wire of square loop is given as

$F_1 = i_2(a)(B$

$F_1 = i_2(a)(\frac{\mu_o i_1}{2\pi x})$

now the force on the other opposite side of the loop is given as

$F_2 = i_2 a B'$

$F_2 = i_2 a (\frac{\mu_o i_1}{2\pi (x + a)}$

Now the net force on the loop due to long current wire is given as

$F = F_1 - F_2$

$F = \frac{\mu_o i_1 i_2 a}{2\pi}(\frac{1}{x} - \frac{1}{a + x})$

$F = \frac{\mu_o i_1 i_2 a^2}{2\pi (x)(x + a)}$

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Topic : magnetic force and mutual inductance

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